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| Fortune From Four (Posted on 2009-11-12) |
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Each of the capital letters in bold denotes a different base ten digit from 0 to 9 to satisfy each of the following alphametic relationships. None of the numbers can contain any leading zero.
(i) ONE is a perfect square and:
(ii) Precisely one of TWO, THREE and FOUR is a perfect square, and:
(iii) Precisely one of TWO + 1, THREE + 1 and FOUR + 1 is a perfect square, and:
(iv) Precisely one of TWO + 2, THREE + 2 and FOUR + 2 is a perfect square.
Determine the number that is represented by FORTUNE.
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Submitted by K Sengupta
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Rating: 5.0000 (1 votes)
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Solution:
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The number represented by FORTUNE is 3701284.
For a detailed explanation, refer to the solution submitted by Benjamin J. Ladd in this location.
*** There was a small typo in Ladd's solution in the 3rd line from the end, and it should be as follows:
FOUR: 3720 (+1 = 61^2) (iii)
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*** Based on a problem by Susan Denham, which appeared on New Scientist No. 1998 (7 Oct 1995), in the Enigma problem section.
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